Let the vector ü = (k,5,-1) and v=(2k,k,3) are perpendicular in R, find the value of k that related with it :

Q: (2) Given u = [2 1 2]T, find a vector v so that the angle between u and v is 60° and the orthogonal…

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Q: What can be said about the vectors u and v when the projection of u onto v equals u?

A: What can be said about the vectors u and v when the eprojection of u onto v equals u?

Q: Find the vector z, given that u = ⟨5, −2, 3⟩, v = ⟨0, 2, 1⟩, and w = ⟨−6, −6, 2⟩.   u − v + w − 2z =…

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Q: Find the vector component of u = ⟨5, 10⟩ that is orthogonal to v = ⟨4, 3⟩, given that…

A: Given,      w1 = projvu = ⟨8, 6⟩   and     u = ⟨5, 10⟩ = w1 + w2.      Where,  u = ⟨5, 10⟩ ,  v =…

Q: Find a nonzero vector orthogonal to the plane through points P(2,1,5), Q(-1,2,3), and R(0,3,3), and…

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Q: Suppose that u, v are vectors in R3 , u · v = 1, ||v|| = 1, the angle between u and v is π/3, and u…

A: The detailed solution is as follows below:

Q: Assume that the vectors u = ai-j+k and w=i+9j+5k orthogonal. Then the are value of a is

A: If two vectors are orthogonal (perpendicular), then their dot product is 0. We use this to solve the…

Q: Find the projection of u onto v and the vector component of u orthogonal to v for u = 3i − 5j + 2k…

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Q: · Let 2 be the separation vector from a fixed point (x', y', z') to the point (x, y, z), and let z…

A: Since r is the separation vector from the point x',y',z' to the point x,y,z and the difference…

Q: Verify that the two planes are parallel. -x + 6y + 2z = 8 -x + 3y + z = 9 2. Find the normal vector,…

A: Find your answer below

Q: Let v be a vector of length 2. If w = -5v, u = (-2, –2) and the angle between w and u is . then v x…

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Q: Find the projection of u onto v and find the vector component of u orthogonal to v. u = ⟨9, 7⟩, v =…

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Q: Consider the vector v = 1 and the vector "function" w(k) = 1 For what value of k are i and w(k)…

A: Two vectors v→ and w→ are said to be orthogonal if v→·w→=0 Given v→=111w→=11k

Q: Find vector u with the magnitude given that satisfies the given conditions. v (7, -1, 3), ||u || -…

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Q: Find a vector v that is perpendicular to the plane through the points А %3 (0, 4, —3), В 3 (5, —5,…

A: Coordinator of the plane is given Find out the vector that is perpendicular to the plane

Q: Find the vector that makes equal acute angles with the positive coordinate axes and has length 2. O…

A: An acute angle is an angle that measure is less than a right angle (90 degrees). The magnitude of a…

Q: Find the vector z, given that u = , v = , and w = . z = 8u - 3V - -W 2 1. Z =

A: We have been given the vectors  u = <1, 2, 3> v = <2, 2, -1> w = <4, 0, -4>

Q: Let v = ( 1, 2 ), Find a vector w with the same direction as v such that || w || = 7.

A: Let v=1,2 Then,  v=12+22=5 The unit vector in the direction of v is, v=vv=1,25=15,25

Q: Prove the stated property of distance between vectors. d(u, v) = 0 if and only if u = v

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Q: Consider the vector v = (−1, 3, 0, 4). Find u such that (a) u has the same direction as v and…

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Q: The vectors T and N, when defined, (a) are parallel. (b) are orthogonal. (c) have a zero cross…

A: T is the tangent vector and N is the normal vector.  So they are always orthogonal to each other.

Q: Consider the vector i 3, and let V 4 = span(ï) C Rº. %3D %3D 5

A: Given: Let the vector V→=12345 and V= span(V→)

Q: Verify that the two planes are parallel. -x + 6y + 3z = 4 1 - x + 2y + z = 5 3 Find the normal…

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Q: Find a vector v that is perpendicular to the plane through the points A = (4, – 5, –2), B = (2,3,…

A: We are asked to find the vector that perpendicular to the plane through the points

Q: The vector y which is collinear with the vector u= and satisfies the condition u.v= 3, is O O O…

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Q: Find a vector v that is perpendicular to the plane containing 3 -() 6 and 0 2

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Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = (4,…

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Q: The vector is orthogonal to the plane 4x + 5y –7z =1 Select one: O True O False

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Q: Given the points X(1, -2, 1) and Y(0, 3, -2), find a vector that is collinear with XY and has a…

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Q: 1. For what value of c is the vector v = = (2,–5, c) orthogonal to w = (3, 2,9)?

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you.  If…

Q: For what value of c is the vector v = ⟨2, -5, c⟩ orthogonal to w = ⟨3, 2, 9⟩?

A: Two vectors are said to be orthogonal if their dot product is zero.

Q: Find the vector w which is of length 6 and oppositely directed to u=(2,-2,1) Select one: O None W=…

A: A vector oppositely directed to  u⇀ = <2,-2,1>  is  w = − u = − <2,-2,1>  i.e.  w =…

Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = ( 5 , −…

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Q: Consider two vectors A and B prove that the cross product between them can be calculated as follows…

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Q: Given the points X(1, -2, 1) and Y(0, 3, -2), find a vector that is collinear with XY and has a…

A: Given: X(1, -2, 1) and Y(0, 3, -2).

Q: Suppose that u, v are vectors in R³, u · v = 1, || = 1, the angle between u and v is T/3, and u is…

A: According to the problem, we have

Q: For which value of k the two vectors u=(3,3,k) and v= (-4,8,1) are orthogonal? *

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Q: By using the definition of the dot product, which vector is orthogonal (perpendicular) to á =…

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Q: For the vector PP, , its norm satisfies PP, =2. The inscribed angles between PP, 2 2 and x-axis and…

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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = ( – 1,…

A: find the explanation below

Q: For any vectorV and unit vector U parallel to V , then D-

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Q: Let the vector ū = (k,5,–1) and v = (2k,k,3) are perpendicular in R', find the value of at related…

A: Given: u→=k,5,-1v→=2k,k,3

Q: 2 -a) Find a unit vector perpendicular to the plane that passes through the points P(1,4, 6), Q =…

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Q: Given the vectors, v = (1,–2,-3) and w = (3,– 2, 1), find the orthogonal projection of v onto w.

A: Since you have posted multiple questions, we answered the first question for you. If you want us to…

Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = (5, 2,…

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Q: Suppose vectors u and v lie in the xy-plane (the z-component of each vector is zero). Now suppose…

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Q: Given the following points in x-y plane: A(0,1), B(1,1), C(2,2), D(0,3), E(1,5), F(3,2), G(2,4),…

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Q: perpendicular to the plane formed by the vectors w1 = [1 2 1] and w2 = [2 2 3], with the z axis

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Q: Consider the vectors H [0] H . If I is the line defined by the vector w₁, fi W1 = [o] W2

A: Here, in the question three vectors are given:  w1, w2, b  L is the line defined by the vector w1 We…